So this took me so many attempts and here it goes:
Find the r values using this formula:
r=sqrt (x^2+y^2)r=√x2+y2
Plug in:
([2sqrt2 (cos45^o + isin45^o)]^5[3sqrt2 (cos135^o + isin135^o)]^3 )/[2(cos 30^o + isin30^o)]^10 [2√2(cos45o+isin45o)]5[3√2(cos135o+isin135o)]3[2(cos30o+isin30o)]10
Power and Multiply:
(2sqrt2)^5(2√2)5 see how I powered the 2sqrt22√2 and you do the same with the rest
((2sqrt2)^5(cos5 times 45^o + isin5 times45^o)(3sqrt2)^3(cos 3 times 135^o +isin3 times 135^o))/(2^10(cos10 times + isin10 times 30))(2√2)5(cos5×45o+isin5×45o)(3√2)3(cos3×135o+isin3×135o)210(cos10×+isin10×30)
Simplify:
(128sqrt2(cos225^o + isin225^o) 54sqrt2(cos405^o + isin405^o))/(1024(cos 300^o + isin 300^o))128√2(cos225o+isin225o)54√2(cos405o+isin405o)1024(cos300o+isin300o)
(13824 (cos630^o + isin630^o)) /(1024(cos300^o + isin300^o))13824(cos630o+isin630o)1024(cos300o+isin300o)
Divide:
27/2272 (cos630^o-300^o + isin630^o-300^o)(cos630o−300o+isin630o−300o)
Simplify:
27/2272 (cos330^o + isin330^o)(cos330o+isin330o)
Which gives your answer . . .